It sounds like you are my mother, writing about me 20 years ago. (Seriously, you just described me at 7) Now that I have finished crying, here's the hard truth. This is going to sound mean, but it's from first hand experience, and I mean well by it. Just parse out the pertinent information, and drop the rest.
There isn't anything you can do to prevent or eliminate this. In my experience, the more you try (as my mother did) the worse you will make it on her. It will continue, and it will get worse with age. Eventually she will infer what the little white lies mean. That's going to hurt, but no matter what you try to do, you won't be able to turn the situation around for her. She will be rejected, hurt, and confused by social interaction with NT's for the next twenty odd years.
Just help her learn how to be alone. Help her learn that other people aren't the thing to cry over. Don't stress her out about human interaction, you'll only compound the problem. (The mental strain of trying to figure out what people are talking about is enough. Pointing out how bad she is at it won't help, but will only drive her to constant anxiety in such situations, much as it did I) That means no more forced play-dates. If it doesn't happen, teach her that that is great, and now she gets to do whatever she wants.
Get her around some other Asperger kids. Focus on one-on-one situations. Go to a museum or something that either of the kids are super interested in. One will start stemming (remember that in general autism, this is expressed in physical movements or ticks, such as rocking, or repeating words. In Asperger's, this tends to be knowledge repetition, expulsion, and subject droning) on the subject, and the other will soak it up... Maybe. You'll have to cycle through a few kids until you get the correct Asperger's pairing. (My best friend Aaron and I randomly met at an airplane museum as kids. I knew everything about WW2 air-frames, and he knew everything about WW2 airplane engines! We were inseparable until his suicide.) The goal of the meeting isn't for play. The goal is for both kids to enjoy it. If that just so happens to turn out to be your daughter and some other kid screaming at each other about what engine went in the P-47C-5, (an R-2800-59 as I recall) who cares!? If they both enjoy it, let it be. It's all they get, and even that won't last forever.
Enjoy the easy times while they last. Puberty won't be fun. College won't be fun. If you are smart enough not to pressure her about people every day, she might even live long enough to figure some things out on her own.